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  "body": "\n## Summary\n\nA Bézier curve is a polynomial curve determined by a finite list of control points, given by the [[Bernstein basis polynomials|0JT92VK307]].\nIt starts at the first control point, ends at the last one, and lies in the [[convex hull|0FQSDC2EQ2]] of all of them.\nBézier curves are the basic curves of vector graphics, fonts and computer-aided design.\n\n## Explanations\n\n### L1 human\n\nPick a start point, an end point, and a few extra points in between that the curve is attracted to but does not have to pass through.\nThe Bézier curve leaves the start point heading toward the second point and arrives at the end point coming from the second to last point.\nMoving one control point changes the curve smoothly everywhere.\nFor three points $P_0, P_1, P_2$ one gets the parabola arc $(1-t)^2 P_0 + 2t(1-t) P_1 + t^2 P_2$.\n",
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